I sure hope somebody comes up with a better solution for you than what I have, because you are in for a bit of work, my friend.

Based on your screenshots, I am going to make an assumption: Every line in your artwork is continuous from start to finish. The ones that go from the top to bottom or left to right (for example) are unbroken, creating the border for several areas along their length.

Because of the complexity of your artwork and what I can see in the screenshot, I cannot give you an exact step-by-step. Instead, I'll have to work on concepts for you that you can then carry on to each area.

Just to give you a quick hands on for what you need to do, let's do a quick exercise.

1) Create a new AI document, no specific settings.
2) Using the line or pen tool, draw a tick-tac-toe board ( # ). The lines can be straight, or you can make them curvy to better see how this will work for your project - the concept is the same.
3) Window > Pathfinder > Divide

What happened is that AI determined where the lines intersected and removed everything 'outside' and made the area a closed path. That *SEEMS* to be what you are after.

It is important to note that the four lines you drew in our example CROSSED OVER each other. In your screenshot, I see a couple of areas that might have gaps. Keep that in mind as we start this next process.

Basically, you are going to have to do this for each territory. Following these instructions, you will be working in one layer, keeping your finished work in another, keeping an original in a third. Naturally, you will be working in a COPY of the original file... :)

A) Have you made and named your layers yet?
B) Look for any gaps in the borders and fix them now. Adjust them so that they CROSS the intersecting border and LEAVE THEM DANGLING in another area. For what we are going to do, it is OKAY and even necessary; they will not be in the finished product.

So, the steps in order for each area:

1) Select ALL of the borders of ONE area. CTRL-C (copy), CRTL-SHIFT-V (paste in place), SELECT your work layer in the layers panel, Object > Arrange > Send To Current Layer. **At this point a copy of all of the borders of ONE area are on a layer all by themselves.
2) Hide the finished and original layers, so all you see are the lines you are working on right now.
3) ENSURE that there are no gaps and all paths cross over each other. **I know, you did it earlier, but let's make absolutely sure right now.
4) Select all the lines (CTRL-A) and Window > Pathfinder > Divide.
5) Unhide your finished work layer, select it in the layers panel, and Object > Arrange > Send To Current Layer.
6) Admire your map as you add each area.
7) Hide your finished work layer, show your original layer and go back to #1 with the next area. Unless you just did the last one. :)

So, you are all done, all of your areas are closed paths on their own layer. NOW you can format them.

This is a lot of work and many interesting concepts for someone new to AI. I hope it helps and you learn a bit.